\Header{tapply}{Apply a Function Over a ``Ragged'' Array}
\keyword{iteration}{tapply}
\keyword{category}{tapply}
\begin{Description}\relax
Apply a function to each cell of a ragged array, that is to each
(non-empty) group of values given by a unique combination of the
levels of certain factors.\end{Description}
\begin{Usage}
\begin{verbatim}
tapply(X, INDEX, FUN = NULL, ..., simplify = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{X}] an atomic object, typically a vector.
\item[\code{INDEX}] list of factors, each of same length as \code{X}.
\item[\code{FUN}] the function to be applied.  In the case of functions like
\code{+}, \code{\%*\%}, etc., the function name must be quoted.  If
\code{FUN} is \code{NULL}, tapply returns a vector which can be used
to subscript the multi-way array \code{tapply} normally produces.
\item[\code{...}] optional arguments to \code{FUN}.
\item[\code{simplify}] If \code{FALSE}, \code{tapply} always returns an array
of mode \code{"list"}.  If \code{TRUE} (the default), then if
\code{FUN} always returns a scalar, \code{tapply} returns an array
with the mode of the scalar.
\end{ldescription}
\end{Arguments}
\begin{Value}
When \code{FUN} is present, \code{tapply} calls \code{FUN} for each
cell that has any data in it.  If \code{FUN} returns a single atomic
value for each cell (e.g., functions \code{mean} or \code{var}) and
when \code{simplify} is \code{TRUE}, \code{tapply} returns a multi-way
\link{array} containing the values.  The array has the same number of
dimensions as \code{INDEX} has components; the number of levels in a
dimension is the number of levels (\code{nlevels()}) in the
corresponding component of \code{INDEX}.

Note that contrary to S, \code{simplify = TRUE} always returns an
array, possibly 1-dimensional.

If \code{FUN} does not return a single atomic value, \code{tapply}
returns an array of mode \code{\Link{list}} whose components are the
values of the individual calls to \code{FUN}, i.e., the result is a
list with a \code{\Link{dim}} attribute.\end{Value}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.\end{References}
\begin{SeeAlso}\relax
the convenience functions \code{\Link{by}} and \code{\Link{aggregate}} 
(using \code{tapply});
\code{\Link{apply}},
\code{\Link{lapply}} with its versions
\code{\Link{sapply}} and \code{\Link{mapply}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
groups <- as.factor(rbinom(32, n = 5, p = .4))
tapply(groups, groups, length) #- is almost the same as
table(groups)

data(warpbreaks)
## contingency table from data.frame : array with named dimnames
tapply(warpbreaks$breaks, warpbreaks[,-1], sum)
tapply(warpbreaks$breaks, warpbreaks[, 3, drop = FALSE], sum)

n <- 17; fac <- factor(rep(1:3, len = n), levels = 1:5)
table(fac)
tapply(1:n, fac, sum)
tapply(1:n, fac, sum, simplify = FALSE)
tapply(1:n, fac, range)
tapply(1:n, fac, quantile)

## example of ... argument: find quarterly means
data(presidents)
tapply(presidents, cycle(presidents), mean, na.rm = TRUE)

ind <- list(c(1, 2, 2), c("A", "A", "B"))
table(ind)
tapply(1:3, ind) #-> the split vector
tapply(1:3, ind, sum)
\end{ExampleCode}
\end{Examples}

